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Empirically observed time series in physics, biology, or medicine, are commonly generated by some underlying dynamical system (DS) which is the target of scientific interest. There is an increasing interest to harvest machine learning…
To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the…
Networks representation aims to encode vertices into a low-dimensional space, while preserving the original network structures and properties. Most existing methods focus on static network structure without considering temporal dynamics.…
Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…
Coherent X-ray scattering (CXS) techniques are capable of interrogating dynamics of nano- to mesoscale materials systems at time scales spanning several orders of magnitude. However, obtaining accurate theoretical descriptions of complex…
We study the problems arising from modeling high-dimensional tensor-valued time series under a Tucker decomposition-based factor model with multiple structural change points. First, we propose an algorithm for detecting the multiple change…
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…
Recently Chen and Poor initiated the study of learning mixtures of linear dynamical systems. While linear dynamical systems already have wide-ranging applications in modeling time-series data, using mixture models can lead to a better fit…
We propose Lagrangian Descriptors (LDs) as a diagnostic framework for evaluating neural network models of Hamiltonian systems beyond conventional trajectory-based metrics. Standard error measures quantify short-term predictive accuracy but…
Understanding the complex interactions within dynamic multilayer networks is critical for advancements in various scientific domains. Existing models often fail to capture such networks' temporal and cross-layer dynamics. This paper…
Reconstructing the attractors of complex nonlinear dynamical systems from available measurements is key to analyse and predict their time evolution. Existing attractor reconstruction methods typically rely on topological embedding and may…
We consider tensor data completion of an incomplete observation of multidimensional harmonic (MH) signals. Unlike existing tensor-based techniques for MH retrieval (MHR), which mostly adopt the canonical polyadic decomposition (CPD) to…
During the past decade, novel Deep Learning (DL) algorithms, workloads and hardware have been developed to tackle a wide range of problems. Despite the advances in workload and hardware ecosystems, the programming methodology of DL systems…
This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and…
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…
Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by…
We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor products of one-dimensional feedforward networks or a linear…
In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical and graphical representations. We discus the concept of…
In this paper we explore how concepts of high-dimensional data compression via random projections onto lower-dimensional spaces can be applied for tractable simulation of certain dynamical systems modeling complex interactions. In such…
Large-scale Dynamic Networks (LDNs) are becoming increasingly important in the Internet age, yet the dynamic nature of these networks captures the evolution of the network structure and how edge weights change over time, posing unique…